cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A110673 Numbers that are neither the sum nor the difference of two primes.

Original entry on oeis.org

23, 37, 47, 53, 67, 79, 83, 89, 93, 97, 113, 117, 119, 121, 123, 127, 131, 143, 145, 157, 163, 167, 173, 185, 187, 203, 205, 207, 211, 215, 217, 219, 223, 233, 245, 247, 251, 257, 263, 277, 287, 289, 293, 297, 299, 301, 303, 307, 317, 321, 323, 325, 327, 331
Offset: 1

Views

Author

Eric Angelini, Sep 14 2005

Keywords

Comments

The sequence is obtained by interleaving A099019 and A134797. From Goldbach's conjecture, apparently all terms are odd. - Bob Selcoe, Mar 10 2015
Intersection of A007921 and A014092. - Michel Marcus, Mar 16 2015

Links

Crossrefs

Cf. A007921 (not the difference), A014092 (not the sum).
Cf. also A099019, A134797.

Programs

  • Mathematica
    Lim=331; nn=PrimePi[Lim+1]; (* Lim is upper limit of sequence; nn is range of primes to consider *)
dif=Union[Flatten[Differences/@Subsets[Prime[Range[nn]],{2}]]]; (* differences of two primes *)
sum=Union[Join[Flatten[Total/@Subsets[Prime[Range[nn]],{2}]],Table[2*Prime[n], {n, nn}]]];seq2; (* sums of two primes *)
Complement[Range[Lim],dif,sum] (* neither sum nor difference *) (* James C. McMahon, Jun 10 2024 *)

Extensions

Corrected and extended by Joshua Zucker, May 04 2006
Offset corrected by Arkadiusz Wesolowski, May 19 2012

A255763 Odd numbers that are not twin primes.

Original entry on oeis.org

1, 9, 15, 21, 23, 25, 27, 33, 35, 37, 39, 45, 47, 49, 51, 53, 55, 57, 63, 65, 67, 69, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 105, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 141, 143, 145, 147, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 183, 185, 187, 189, 195, 201
Offset: 1

Views

Author

Omar E. Pol, Mar 30 2015

Keywords

Comments

UNION of A014076 and A134797.

Crossrefs

Cf. A001097, A005408, A014076, A134797.

A085434 Twice odd isolated primes.

Original entry on oeis.org

46, 74, 94, 106, 134, 158, 166, 178, 194, 226, 254, 262, 314, 326, 334, 346, 422, 446, 466, 502, 514, 526, 554, 586, 614, 634, 662, 674, 706, 718, 734, 746, 758, 766, 778, 794, 802, 818, 878, 886, 898, 914, 934, 958, 974, 982, 998, 1006, 1018, 1082, 1094
Offset: 6

Views

Author

Cino Hilliard, Aug 13 2003

Keywords

Comments

Name was: n-th even number not a power of 2 whose largest and smallest factors do not add or subtract to a twin prime. - Robert Israel, Mar 11 2025
The density of these numbers approach 0 as n approaches oo.

Crossrefs

Cf. A052369, A056608, A134797.

Programs

  • Maple
    P:= select(isprime, {seq(i,i=3..1000,2)}):
A:= P minus (P +~ 2) minus (P -~ 2):
sort(convert(A,list)) *~ 2; # Robert Israel, Mar 11 2025
  • PARI
    maxpmmintwin(n) = { c=0; forprime(p=3,n, if(!isprime(p-2) & !isprime(p+2),print1(p+p","); c++); ); print(); print(c" "c/n+.0) }

Formula

a(n) = 2 * A134797(n).

Extensions

Definition corrected by Robert Israel, Mar 11 2025

A322842 Primes p such that both p+2 and p-2 are neither prime nor semiprime.

Original entry on oeis.org

173, 277, 457, 607, 727, 929, 1087, 1129, 1181, 1223, 1237, 1307, 1423, 1433, 1447, 1493, 1523, 1549, 1597, 1613, 1627, 1811, 1861, 1973, 2011, 2063, 2137, 2297, 2347, 2377, 2399, 2423, 2677, 2693, 2753, 2767, 2797, 2819, 2851, 2917, 3023, 3313, 3323, 3449
Offset: 1

Views

Author

Kyle Buscaglia, Cory Baker, Dec 28 2018

Keywords

Comments

Also: Primes p such that both p+2 and p-2 have at least three prime divisors. - David A. Corneth, Dec 28 2018

Links

Crossrefs

Cf. A000040, A001358, A007510, A134797.

Programs

  • Java
    boolean isIsolatedPrime(int num){
    int upper = num + 2;
    int lower = num - 2;
    return isPrime(num) &&
          !isPrime(upper) &&
          !isPrime(lower) &&
          !isSemiPrime(upper) &&
          !isSemiPrime(lower);
   }
  • Maple
    q:= n-> numtheory[bigomega](n)>2:
a:= proc(n) option remember; local p;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if q(p-2) and q(p+2) then break fi
      od; p
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Dec 28 2018
  • Mathematica
    Select[Prime[Range[1000]], PrimeOmega[#-2] > 2 && PrimeOmega[#+2] > 2&] (* Jean-François Alcover, Nov 26 2020 *)
  • PARI
    is(n) = isprime(n) && bigomega(n + 2) > 2 && bigomega(n - 2) > 2 \\ David A. Corneth, Dec 28 2018

A130973 Number of primes between successive pairs of twin primes, for a(n) > 0.

Original entry on oeis.org

1, 1, 2, 1, 4, 3, 4, 2, 1, 3, 1, 2, 3, 10, 4, 7, 4, 3, 2, 1, 2, 18, 2, 2, 17, 1, 2, 6, 9, 3, 1, 1, 1, 8, 3, 2, 15, 1, 4, 1, 1, 7, 7, 4, 4, 3, 4, 1, 1, 7, 2, 5, 1, 5, 18, 2, 5, 4, 3, 1, 5, 1, 18, 12, 2, 8, 1, 4, 2, 5, 4, 1, 1, 1, 9, 10
Offset: 1

Views

Author

Omar E. Pol, Aug 23 2007

Keywords

Comments

a(k) corresponds to the k-th term in the isolated prime sequence A007510 or A134797. a(1) corresponds to 23. a(2) corresponds to 37. a(3) corresponds to 47 and 53. - Enrique Navarrete, Jan 28 2017
Lengths of the runs of consecutive integers in A176656. - R. J. Mathar, Feb 19 2017

Links

Crossrefs

Cf. A001223, A007510 (isolated primes), A027883, A048614, A048198, A052011, A052012, A061273, A076777, A073784, A082602, A088700, A179067 (clusters of twin primes).
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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